<?php
/**
 * <https://y.st./>
 * Copyright © 2018 Alex Yst <mailto:copyright@y.st>
 * 
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
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 * 
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this program. If not, see <https://www.gnu.org./licenses/>.
**/

$xhtml = array(
	'<{title}>' => '<em>*sigh*</em>',
	'takedown' => '2017-11-01',
	'<{body}>' => <<<END
<section id="drudgery">
	<h2>Drudgery</h2>
	<p>
		My discussion post for the day:
	</p>
	<blockquote>
		<p>
			Were we to use different definitions for the pres() and lady() functions, we could easily define both the pres ◦ lady composite and the lady ◦ pres composite.
			However, as defined, this isn&apos;t possible.
			By the definitions used for this discussion, pres() takes a date and outputs a name.
			On the other hand, lady() takes a name as input and outputs another name.
			pres ◦ lady, which can be rewritten as pres(lady(x)), is invalid because the output of lady() is a name while the input to pres() must be a date.
			However, lady ◦ pres is completely reasonable, as the name output by pres() is exactly a name in the domain of lady(), so the name output works perfectly well as input to the next function.
		</p>
		<p>
			pres<sup>-1</sup>() would take a president&apos;s name and return the date they&apos;re in office.
			Except ... presidents are usually in office for more than one day.
			While we&apos;re not working with numbers in this discussion, pres<sup>-1</sup>() is analogous to a &quot;function&quot; in which more than one y value is paired with the same x value.
			That makes pres<sup>-1</sup>() <strong>invalid</strong>.
		</p>
		<p>
			lady<sup>-1</sup>() would take a first lady&apos;s name and return the name of the president they served with.
			Assuming each first lady only serves with one president (no remarriages, et cetera) and all names are unambiguous (middle names are included to avoid situations such as George Herbert Walker Bush and George Walker Bush both being called &quot;George Bush&quot;), this function would be <strong>valid</strong>.
		</p>
		<p>
			(lady ◦ pres)<sup>-1</sup>() would take a first lady&apos;s name as input and output the date that they served.
			But, as before, terms of service last longer than a day.
			You can&apos;t invert the pres() function, so you can&apos;t invert a composite pres() function.
			(lady ◦ pres)<sup>-1</sup>() is <strong>invalid</strong>.
		</p>
		<p>
			(pres ◦ lady)<sup>-1</sup>() ...
			What would that even do?
			As discussed previously, pres ◦ lady is invalid.
			How are we supposed to invert a function that is itself undefined?
			(pres ◦ lady)<sup>-1</sup>() is therefore <strong>invalid</strong>.
		</p>
	</blockquote>
</section>
END
);
